Hi, Iildude.
There is no word as Ake Ittsai (明け一才)
Before the end of Ittsai(一才)=tosai, They are called Ake Nisai (about 8-12 month old) or many guys in Japan still call them simply Tosai.
As soon as the end of Ittsai (一才)= Ake Nisai by June of next year, then Nisai (二才)
Additional Trivia :

Baby fry is called Kego(毛仔). then Chigyo(稚魚). then Tosai(当才). then Ake Nisai (明け二才). then Nisai (二才)
Bye